Equations

2t - 3 is an expression. It becomes an equation when it is set equal to another expression. So 2t - 3 = 0 is an equation
as is y = 4r + 2 Another word for the last equation is function and we usually substitute f(x) for y. So f(x) = 4r + 2

The domain of an expression or function is the values that can be substituted in for the variables in this case t or r.
The domain of the above expression and equations is all real numbers.

The solution set, which comes from the domain, for the equation  y = 4r + 2 is all real numbers.
The solution set for the equation 2t - 3 = 0 is 3/2
No other number makes that equation a true statement and hence the solution set for this equation is one term.
When graphing a function the horizontal axis is usually the domain of the function.

When you are asked to solve an equation you are being asked to find the number or numbers that make the equation true.
This number or numbers is the solution set and each term of the set is called a root or solution.

Other terms to describe equations are equivalent, conditional and identity.

• equivalent means that equations have the same solutions
• conditional means that only certain values from the domain are solutions
• identity means that all values from the domain are solutions

Try these examples:

1. 4r + 7 = 0    answer
2. 3t - 7 = 4t + 29   answer
3. (1/4)p + (2/3)p + (4/9) = 0   answer
4. 4 + 6(12k - 4) = .4(4k - 16) - 3    answer
5. (tan (p))(cot(p)) = 1   answer
6. 3/t + 4/5 = 5 + 5/7t   answer

2 +

3x + 5    2

=

5x + 1    3

answer

t + 7    t + 2

= - 4 +

8t + 1    t + 2

answer



9. A plumber can finish a job in 7 hours. Working with another plumber the job takes 4 hours.
   How long would it take the second plumber to complete the job working alone?    answer


10. You purchase a TV for for $149 and sell it at a loss for $111. Approximately what percentage have you loss?    answer

Question # 1 is a linear equation. If you graph it the result will be a straight line. You can tell it is a linear equation
because the variable r has an exponent is 1. Stated mathematically the degree of the equation is one.

Question # 2 is a quadratic equation. If you graph it the result will be a parabola. You can tell it is a quadratic equation because
the variable t has an exponent is 2. Stated mathematically the degree of the equation is two.

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